Estimating the Magnitude of Completeness and its Uncertainties

Abstract

Earthquake catalogs are not complete over the entire range of magnitudes. A preliminary step that should be performed before any seismicity and hazard-related studies is to assess the quality, consistency and completeness of the earthquake catalogs. This can be achieved by assessing a threshold magnitude called magnitude of completeness, Mc, defined as the lowest magnitude above which all the magnitudes follow Gutenberg-Richter law(GR law). Assessing Mchave received considerable attention in the last few decades. In general, most of the catalog based methods are deployed by fitting GR law fit the observed Frequency magnitude distribution (FMD) of the earthquake magnitudes. Although, the limitation of these methods in estimating Mc is that they fail in the case of less number of events in the catalog. We propose new catalog-based methods would work even with less number of events in the catalog. The stochastic method used for generating the synthetics for testing the method was by modelling the FMD using the probability density function(pdf) of the normal distribution to model FMD below Mcand GR law for magnitudes greater than or equal to Mc. The best estimate of Mcwas drawn from a set of assumed Mc by using two methods. We check which of these assumed Mc's satisfies the criteria of method 1) KS distance approach and method 2) maximum probability approach, by comparing original FMD with the modelled FMD. A comparative analysis was carried out to check the performance of the proposed methods with those of three existing catalog based methods, using generated synthetics. Furthermore, we are planning to develop synthetic catalog by incorporating the uncertainties associated with the earthquake magnitudes. In addition, we are focussed to come up with realistic synthetic catalogs which carry the spatial and temporal similarity with the catalog.